Solving Numerical Problems on Demand, Elasticity, and Cost

Numerical Problems on Demand

Example 1 Demand Function

Given demand function
Qd = 50 − 2P

Find quantity demanded when price is 10.

Solution

Qd = 50 − 2 × 10
Qd = 50 − 20
Qd = 30 units

Answer

Quantity demanded is 30 units.

Example 2 Law of Demand:

Price of a good falls from 8 to 6 and quantity demanded rises from 20 to 30.

This shows inverse relationship between price and demand, so law of demand is satisfied.

Numerical Problems on Price Elasticity of Demand

Formula

PED = Percentage change in quantity demanded ÷ Percentage change in price

Example 1 PED using percentage method

Price falls from 10 to 8
Quantity demanded rises from 20 to 30

Step 1 Change in Quantity

Change in Q = 30 − 20 = 10
Percentage change in Q = 10 ÷ 20 × 100 = 50%

Step 2 Change in Price

Change in P = 8 − 10 = −2

Percentage change in P = −2 ÷ 10 × 100 = −20%

Step 3 PED

PED = 50 ÷ 20 = 2.5

Answer

Demand is elastic.

Example 2 PED using total expenditure method

Price falls and total expenditure rises.

So demand is elastic.

Numerical Problems on Income Elasticity of Demand

Formula

YED = Percentage change in quantity demanded ÷ Percentage change in income

Example

Income rises from 20,000 to 24,000

Demand rises from 10 units to 14 units

Step 1 Percentage change in Quantity

Change = 4

Percentage = 4 ÷ 10 × 100 = 40%

Step 2 Percentage change in Income

Change = 4,000

Percentage = 4,000 ÷ 20,000 × 100 = 20%

Step 3 YED

YED = 40 ÷ 20 = 2

Answer

YED is positive and greater than 1

The good is a luxury good.

Numerical Problems on Cross Elasticity of Demand

Formula

XED = Percentage change in quantity of A ÷ Percentage change in price of B

Example

Price of tea rises by 10%

Demand for coffee rises by 20%

XED = 20 ÷ 10 = +2

Answer

XED is positive

Tea and coffee are substitutes.

Numerical Problems on Cost

Given Data

Marginal Cost

Formula

MC = Change in Total Cost ÷ Change in Output

MC from 1 to 2 units

MC = 180 − 100 = 80

MC from 2 to 3 units

MC = 270 − 180 = 90

Average Cost

Formula

AC = Total Cost ÷ Output

At 2 units

AC = 180 ÷ 2 = 90

At 3 units

AC = 270 ÷ 3 = 90